Scalar field dark matter with two components: combined approach from particle physics and cosmology

We explore the possibility of incorporating particle physics motivated scalar fields to the dark matter cosmological model, along with the successful modeling performed by the classical complex scalar field and without spoiling the advantages that this model gives, particularly, the one related to the existence of certain region in the parameter space, which increases the number of neutrino species $N_{\text{eff}}$ in the correct amount needed in the early Universe to be consistent with the observed abundance of light elements produced at Big Bang Nucleosynthesis (BBN). We also examine the differences between these models and the priors considered at the edges of the cosmic ladder obtaining that they have a clearly different behavior depending on the combination of the two scalar fields taken into account. In such cases we obtain that depending on the value of the Hubble constant inferred from CMB Planck 2018 data or considering a local value of this constant we can notice a different distribution of matter densities at early or late epochs. We take as a first example, one of the Higgs-like candidates of dark matter and show that if it is added along with the classical complex scalar field, it will give consistent results within the BBN constrain if the heavy scalar field composes less than $58\%$ of the total dark matter. We also use an axion field which has negative self interaction then we will show that (as long as the symmetry breaking scale $f_a$ is below the Planck scale) there will be at least a region for which the two-field system is consistent with the constrains. Finally we will explore the possibility of combining the axion and Higgs-like scalar fields and show that there is no set of parameters that allows to be consistent with $N_{\text{eff}}$ from BBN constraints. Our results could be relevant on the direct dark matter detection programs.